Nonlinear least squares

The estimation methodology so far is linear least squares. First we found a spatial predictor on a mesh. Then we introduce missing data by interlacing the mesh on both axes. Then we assert the two-dimensional filter is a dip filter and that it is appropriate for use on the doubly refined mesh. With this operator, we then solve the linear least squares problem for the missing data.

We made an approximation when we presumed the 2D filter was essentially a dip filter and that the imperfect coherency was not significant. Now is the time to patch up that approximation by solving the nonlinear least-squares problem allowing both the filter and the missing data to readjust on the principle that the output power be minimized. Presumeably we are already close to the solution so we can expect rapid convergence.